Analysis of bulk queue with additional optional service, vacation and unreliable server

The present investigation deals with the performance analysis of group input queueing system with unreliable server. The server is capable of rendering essential as well as optional services. After getting essential service, the customer may choose any one of the available optional services if required. The server has choice either to avail the vacation for the short period after completion of the service or may continue to provide the service to other customers. The server may fail at any instant of the essential/optional service and undergoes repair immediately. The queueing model is developed by introducing the supplementary variables corresponding to elapsed setup time, service time, and repair time and vacation duration for obtaining the queue size distribution. The maximum entropy principle is employed to determine the approximate results of the system state probabilities and the waiting time of the customers in the queue. The numerical simulation and sensitivity analysis are performed by taking the numerical illustration to study the effect of system parameters on the various performance measures and cost function.